论文标题
与依赖的高斯混合模型中的社区检测精确恢复
Exact Recovery of Community Detection in dependent Gaussian Mixture Models
论文作者
论文摘要
我们在高斯混合模型上研究了社区检测问题，其中（1）顶点分为$ k \ geq 2 $不同的社区，这些社区不一定是同等规模的； （2）观察矩阵中不同条目的高斯扰动不一定是独立或相同分布的。我们证明了最大似然估计（MLE）的精确恢复的必要条件，并讨论这些必要和充分条件给出尖锐阈值的情况。应用程序包括在图上的社区检测，在每个边缘上观察值的高斯扰动是其末端顶点上的i.i.d.〜高斯随机变量的总和，在其中，我们明确地获得了MLE的精确恢复的阈值。
We study the community detection problem on a Gaussian mixture model, in which (1) vertices are divided into $k\geq 2$ distinct communities that are not necessarily equally-sized; (2) the Gaussian perturbations for different entries in the observation matrix are not necessarily independent or identically distributed. We prove necessary and sufficient conditions for the exact recovery of the maximum likelihood estimation (MLE), and discuss the cases when these necessary and sufficient conditions give sharp threshold. Applications include the community detection on a graph where the Gaussian perturbations of observations on each edge is the sum of i.i.d.~Gaussian random variables on its end vertices, in which we explicitly obtain the threshold for the exact recovery of the MLE.
